Possible Reinforcements of RSA and Some Other Encryption Methods

Abstract

This paper explores potential reinforcements of the RSA algorithm and examines several alternative public-key cryptosystems. Building on the mathematical foundation of integer factorization, RSA has been the cornerstone of secure digital communication, yet it faces vulnerabilities from parameter weaknesses and emerging quantum algorithms. To address efficiency and resilience, this study first analyzes multi-prime RSA, highlighting its advantages in decryption speed through the Chinese Remainder Theorem, while also noting its reduced security margins. In addition, the Goldwasser–Micali cryptosystem is evaluated for its probabilistic encryption mechanism, which enhances semantic security by producing randomized ciphertexts. The LUC encryption scheme, based on Lucas sequences, is then discussed as a variant of RSA with potentially stronger resistance against certain attacks. Finally, an algebraic encryption method utilizing polynomial roots is introduced as an innovative approach, though its practical security remains uncertain. Collectively, these explorations illustrate the trade-offs between efficiency, ciphertext size, and security, and point toward future directions in strengthening public-key cryptography against advancing computational threats.